Events

Analysis and Applied Math Seminar

This page contains the calendar of events for the Analysis and Applied Math Seminar at the University of Toronto. The seminar meets regulary on Fridays, 1:10 - 2 pm, Room 6183 in the Bahen Centre. For more information, please contact one of the organizers: Robert Jerrard or Amir Moradifam.

Details

A semiclassical proof of Quillen's theorem

by
Maciej Zworski
|
University of California at Berkeley
Time: 13:10 (Friday, Sep. 09, 2011)Location: BA6183, Bahen Center, 40 St. George St.Abstract:
In this expository talk I give a semiclassical interpretation of Quillen's original proof of his 1968 theorem on decomposition of positive complex bi-homogeneous forms into sums of Hermitian squares. The result can be interpreted as a hermitian analogue of Hilbert's 17th problem and it was rediscovered by Catlin and D'Angelo in 1996. Both proofs are related to the Fourier–Bros–Iagolnitzer transform (FBI) transform, quantum harmonic oscillator and the calculus of Toeplitz operators.